Sample Size Estimation Through Simulation of a Random Coefficient Model

In chronic pulmonary diseases, the development of emphysema progresses over many years. As a result, the assessment of drug efficacy requires the observation of large numbers of patients, followed for long periods of time. Recently, lung densitometry has been studied as a potential clinical endpoint for the assessment of lung tissue loss over time in patients with emphysema. Clinical trials using lung densitometry as an endpoint are typically designed as longitudinal studies with repeated measurements at fixed time points. Since lung density measurements are generally correlated with lung volume measurements, lung volume should be included in statistical analyses as a longitudinal covariate. The clinical efficacy of treatments can be assessed by comparing the progressions of decreased lung densities through the use of a random coefficient model – a longitudinal linear mixed model with a random intercept and slope. However, the implementation of such complex statistical analyses in clinical trials makes sample size calculations difficult. In this article, an empirical approach to sample size calculations is proposed using simulated trajectories of lung densities and lung volumes. We present step-by-step details for sample size calculations using simulations, and discuss the pros and cons of this approach. SAS Macros are provided.